x*4+8x*2+1=5x(x*2+1)

Solution for x*4+8x*2+1=5x(x*2+1) equation:

x*4+8x*2+1=5x(x*2+1)

We move all terms to the left:

x*4+8x*2+1-(5x(x*2+1))=0

Wy multiply elements

4x+16x-(5x(x*2+1))+1=0


We calculate terms in parentheses: -(5x(x*2+1)), so:

5x(x*2+1)

We multiply parentheses

10x^2+5x

Back to the equation:

-(10x^2+5x)


We add all the numbers together, and all the variables

20x-(10x^2+5x)+1=0

We get rid of parentheses

-10x^2+20x-5x+1=0

We add all the numbers together, and all the variables

-10x^2+15x+1=0

a = -10; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·(-10)·1
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{265}}{2*-10}=\frac{-15-\sqrt{265}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{265}}{2*-10}=\frac{-15+\sqrt{265}}{-20}
$